1. Field of the Invention
The invention relates to a nonlinear precoding method based on a modulo arithmetic for the transmit-side preequalization of K user signals to be transmitted at the same time and frequency in a digital broadcast channel with known transmission behavior set up between a central transmitting station and K decentralized, non-interconnected receiving stations, user signals consisting of data symbols ak with k from 1 to K from an Mk-level signal constellation having a signal point spacing Ak with a periodic multiple representation of the undisturbedly transmitted data symbols ak in data symbol intervals congruent for K receive-side modulo decision devices, a transmit-power-minimizing selection of representatives vk from the range of values ak+Ak·Mk·zkk where zkk is from the set of integers, and linear preequalization of the selected representatives vk to form transmit signals xk to be transmitted.
2. Description of the Related Art
In a broadcast channel, a plurality of user signals present at a common (i.e. central) transmitter (e.g. a base station) are digitally transmitted to a plurality of decentralized (i.e. scattered over a service area) receivers (e.g. mobile stations). Signal transmission user signal → receive signal is unidirectional in the downlink. The particular feature of signal transmission in a broadcast channel is the lack of cooperability between the individual receivers. At no receiver are the signals of the other receivers known, and communication between the individual receivers is not possible. Consequently there can be no joint data processing of the receive signals in a central receiver. Transmission-improving signal conditioning can therefore only take place at the transmit side in the common transmitter. Signal transmission can be wireline, but tends to be non-wireline. The essential but imperfect differentiation of the signals for correct assignment of each user signal to the associated receiver is performed by Code Division Multiple Access (CDMA) or by Space Division Multiple Access (SDMA). The resulting overall structure with a large number of signal inputs (user signals) and a large number of signal outputs (receive signals) is known as a MIMO system (Multiple Input Multiple Output). Moreover, in the case of non-wireline signal transmission (radio transmission), multi-antenna systems are being increasingly used in which the signals are transmitted via a large number of transmitting antennas to a large number of receiving antennas, the numbers of antennas possibly being the same or different and having an impact on signal processing. In general, time and space diversity can be advantageously utilized in a MIMO system.
The problem arising from a plurality of receivers being supplied from a common transmitter is that the individual users are supplied not only with their own wanted signals, but that other users' signals are superimposed thereon, resulting in interference signals. The occurrence of crosstalk interferences is synonymous with loss of the orthogonality which would be present in the case of ideal transmission behavior with decoupled subchannels. On the transmit side it must therefore be attempted, knowing the user signals and the transmission conditions currently obtaining in the broadcast channel, i.e. the individual crosstalk factors between the individual users, to generate a suitable common transmit signal in such a way that each user receives his desired signal but without interference from the other signals. In contrast to the twin problem of the multiple access of scattered transmitters to a common receiver (uplink) for which many approaches are now known, the literature only contains a small number of methods for solving the described problem of serving spatially separated, non-cooperating receivers from a common transmitter. The described transmission scenario can be expressed in a mathematically compact and general manner using the well-known channel equationy=Hx+n 
The possibly already preprocessed transmit symbols of the K users are combined in the vector x=[x1, x2, . . . , xK]T (vector and matrix notation in bold). The complex-valued elements hkI of the channel matrix H describe the couplings between the transmission paths I→k, i.e. the crosstalk of the user I onto the user k. The ideal channel matrix H without couplings is a diagonal matrix, preferably an identity matrix (value 1 on the main diagonal). The channel matrix H can be estimated by various known methods with backchannel or, in the case of duplexing with time division multiplex, also without backchannel and is assumed to be known at the central transmitter (presence of the so-called Channel State Information CSI). Combined in the vector n are the unavoidable noise effect (additive noise) of the electronic components involved and other external interference, and the elements of the vector y=[y1, y2, . . . , yK]T are the receive symbols at the individual receivers. The first known approach for a broadcast channel involves linear preequalization of the user signals (Linear Channel Inversion LCI). From the users' data signals ak present, combined in the vector a, the transmit symbols xk (the term “symbol” in this context means a real or complex number representing the information) are formed according tox=H−1a 
where H−1 represents the inverse matrix to H, which can only be formed, however, if the transmission matrix is non-singular (determinant of the matrix is non-zero). it is achieved, however, that no interference signals are produced at the receivers and the data symbols ak appear directly (with only additive noise superimposed). There is therefore complete decoupling of the individual direct transmission paths k→k (orthogonality). However, the disadvantage of this procedure is the associated, in some cases very substantial, increase in the average transmit power required. This effect is greater the more strongly the matrix H−1 tends to a singular matrix.
A significant increase in the average transmit power is avoided if, instead of linear preprocessing of the user signals, joint nonlinear preequalization (preceding method) is used. With the known preceding methods, however, the mutual interference signals are likewise completely suppressed, so that diversity reception cannot be utilized. Precoding methods can be developed from the twin problem to this situation, i.e. the multiple access scenario (multiple access problem e.g. in the uplink transmit direction in which a plurality of distributed users access a common receiver). There, nonlinear equalization can be performed by successive elimination of the interference signals which is implemented, for example, in the known V-BLAST method and can be termed Zero Forcing Decision Feedback Equalization (ZF-DFE) completely eliminating (Zero Forcing ZF) the interference signals. An established preceding method is known according to Tomlinson and Harashima (THP—Tomlinson-Harashima Precoding) and is based on the use of modulo arithmetic. This procedure is described for the first time by M. Tomlinson in publication I “New Automatic Equaliser Employing Modulo Arithmetic” (Electronics Letters, vol. 7, Nos. 5/6, pp. 138-139, March 1971) and by H. Harashima and H. Miyakawa in publication II “Matched Transmission Technique for Channels with Intersymbol Interference” (IEEE Transactions on Communications, Vol. com. 20, No. 4, pp. 774-780, August 1972). Originally the nonlinear precoding methods were only designed for channels with one input and one output, but with intersymbol interference (ISI) present. It was later recognized that they could also be used on MIMO channels in order to suppress interchannel interference (ICI) or a combination of ISI and ICI. This transmission is described in detail, with the coining of the term MIMO preceding, in publication III by R. Fischer et al. “Space-time Transmission using Tomlinson-Harashima-precoding” (Proceedings of 4. ITG Conference on Source and Channel Coding, pp. 139-147, Berlin, January 2002).
This preequalization can be used in the central transmitter instead of receive-side feedback equalization which is only possible in the case of a central receiver. To ensure that the average transmit power is not significantly increased in the process, THP operates on a nonlinear basis. Here modulo reduction with a sawtooth characteristic limits the transmit signal xk to the range (−Mk/2, +Mk/2] at a level number Mk of the signal constellation selected for the relevant data symbol ak and a selected signal point spacing Ak=1. It should be pointed out at this juncture that in principle a separate level number Mk and a separate signal point spacing Ak can be selected for each data stream to be transmitted. In general, however, for the sake of simplicity these parameters are selected identically for all the user signals to be transmitted. For any given data signals, the output signal is constantly held between predefined modulo limits by a simple addition rule, by which the transmit power can be significantly reduced compared to linear methods. This limiting is performed symbol-by-symbol without memory and is equivalently representable as the addition of a correction symbol which may assume an integral multiple of Ak·Mk. The now apparently linear preequalization in this approach completely nullifies the channel distortion. Essentially with THP, by multiple representation of the data symbols ak and selection of suitable representatives vk which are then linearly preequalized, the transmit signal is therefore formed according to x=H−1v so that any appreciable increase in the average transmit power can be avoided. By the multiple representation and selection of a suitable representative vk, one more degree of freedom is therefore provided for signal processing. In the case of binary transmission, the binary symbols “0” and “1” can be represented e.g. by the amplitude values of +0.5 and −0.5 (signal point spacing Ak=1), corresponding to an Mk=2-level signal constellation. On the basis of the amplitude values selected, when using precoding the binary symbol “0” can, for example, be represented by . . . −3.5; −1.5; +0.5; +2.5; +4.5; . . . and the binary symbol “1” by . . . −2.5; −0.5; +1.5, +3.5; +5.5; . . . with a respective addition of an integer (multiple of Mk=2). With knowledge of all the user data symbols ak (having the values +0.5 and −0.5), the representatives vk (from the range of values (+0.5+2z) where z is a positive or negative integer) are then selected such that, after linear preequalization of the channel, the transmit signal x=H−1v possesses a low average power or smallest possible amplitude.
The related art on which the present invention proceeds is disclosed in publication IV of R. Fischer et al.: “MIMO-Precoding for Decentralized Receivers” (Proceedings of International Symposium on Information Theory—ISIT 02, Lausanne, Switzerland, June/July 2002, p. 496). In continuation of publication III, a modified THP using nonlinear modulo arithmetic is described for a broadcast channel with downlink scenario in which the decentralized receivers have no contact with one other. The transmit-side nonlinear preprocessing can be derived from DFE and has, in mathematical terms, a unitary matrix F operated in the forward direction whose function is to transform the channel matrix into triangular form, and a matrix B present in the nonlinearly operating feedback loop in the form of a lower triangular matrix with unit main diagonal. If the overall channel matrix for the transmission behavior is of triangular form, the interference signals occurring can be precompensated bit by bit in the feedback branch of the central transmitter using modulo arithmetic. At the individual receivers, the data then appears as if the other users (with parallel transmission paths to the other receivers) did not exist.
As mutual interference signals are therefore completely avoided also when using nonlinear precoding methods, in each receiver the transmitted data symbols ak can be recovered or estimated values for them can be formed by threshold decision-making which takes account of the periodic continuation of the amplitude values or signal point spacings (modulo decision device). However, the disadvantage of these preceding methods is that no “diversity gain” can be achieved because of the complete prevention of mutual interference signals. Each transmission subsystem (one user signal to the associated receiver) functions as if it is operated via a separate channel (with one input and output). Specifically in the case of fading channels this involves a high error rate at times of poor transmission conditions. However, if signals are jointly processed and transmitted, a diversity gain can in principle be achieved. If in the case of two transmission paths one of them has poor transmission conditions, it is highly probable that the other transmission path is quite usable.